A259565 a(1) = 1, for n > 1 a(n) = smallest number not already in the sequence such that the arithmetic mean of two neighboring terms is a squarefree number.

1, 3, 7, 5, 9, 11, 15, 13, 17, 21, 23, 19, 25, 27, 31, 29, 33, 35, 39, 37, 41, 43, 49, 45, 47, 55, 51, 59, 57, 53, 61, 63, 67, 65, 69, 71, 75, 73, 81, 77, 79, 85, 87, 83, 89, 93, 95, 91, 97, 105, 99, 103, 101, 109, 111, 107, 113, 115, 121, 117, 119, 125, 129

Offset

1,2

Comments

A259605(n) = (a(n) + a(n+1)) / 2;

conjecture: sequence is a permutation of the odd numbers;

a(A259570(n)) = 2*n-1.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Prog

(Haskell)
import Data.List (delete)
a259565 n = a259565_list !! (n-1)
a259565_list = 1 : f 1 [3, 5 ..] where
   f x zs = g zs where
     g (y:ys) = if a008966 ((x + y) `div` 2) == 1
                   then y : f y (delete y zs) else g ys

Crossrefs

Cf. A086517, A259260, A259429, A259542, A008966, A005117, A005408, A259570.

Cf. A259605.

Sequence in context: A019809 A305741 A021270 * A113910 A264983 A265341

Adjacent sequences: A259562 A259563 A259564 * A259566 A259567 A259568

Keyword

nonn

Author

Reinhard Zumkeller, Jun 30 2015

Status

approved